answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MrRissso [65]
2 years ago
12

Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. the distribut

ion of the population is unknown. the mean and the standard error of the distribution of sample means are
Mathematics
1 answer:
OleMash [197]2 years ago
5 0

Answer:

The mean is 180.

The standard error is 0.286.

Step-by-step explanation:

This question can be solved using the central limit theorem.

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

In this problem, we have that:

The mean of the distribution of the sample means is the same as the mean of the population. This means that the mean is 180.

The standard deviation of the population is the square root of the population variance. So \sigma = \sqrt{196} = 14.

The standard deviation of the sampling distribution of the sample mean is s = \frac{\sigma}{\sqrt{n}} = \frac{14}{\sqrt{49}} = 2.

The standard error of the sampling distribution of the sample mean is SE = \frac{s}{\sqrt{n}} = \frac{2}{7} = 0.286

You might be interested in
Evaluate ∫SF⃗ ⋅dA⃗ , where F⃗ =(bx/a)i⃗ +(ay/b)j⃗ and S is the elliptic cylinder oriented away from the z-axis, and given by x2/
Norma-Jean [14]

Answer:

Therefore surface integral is \pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c.

Step-by-step explanation:

Given function is,

\vec{F}=\frac{bx}{a}\uvec{i}+\frac{ay}{b}\uvec{j}

To find,

\int\int_{S}\vec{F}dS  

where S=A=surfece of elliptic cylinder we have to apply Divergence theorem so that,

\int\int_{S}\vec{F}dS

=\int\int\int_V\nabla.\vec{F}dV

=\int\int\int_V(\frac{b}{a}+\frac{a}{b})dV  

=\frac{a^2+b^2}{ab}\int\int\int_VdV

=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}

=\frac{a^2+b^2}{ab}\times \pi ab\times 2c=\pi (a^2+b^2)c

  • If unit vector \cap{n} directed in positive (outward) direction then z=c and,

\int\int_{S_1}\vex{F}.dS_1=\int\int_{S_1} . dA      

=\int\int_{S_1}.dA=0

  • If unit vector \cap{n} directed in negative (inward) direction then z=-c and,

\int\int_{S_2}\vex{F}.dS_2=\int\int_{S_2}. -dA      

=\int\int_{S_2}. -dA=0

Therefore surface integral without unit vector of the surface is,

\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c

5 0
2 years ago
What is the value of x if g^x-1-2= 25?
SVETLANKA909090 [29]

Answer:

Third option: x=\frac{5}{2}

Step-by-step explanation:

<h3> The correct exercise is attached.</h3>

The equation given is:

9^{x-1}-2=25

 The steps to find the value of "x" are shown below:

1. Add 2 to both sides of the equation:

9^{x-1}-2+2=25+2\\\\9^{x-1}=27

2. Descompose 9 and 27 into their prime factors:

9=3*3=3^2\\27=3*3*3=3^3

3. Substitute them into the equation:

3^{2(x-1)}=3^3

4. Knowing that If a^n=b^m, then n=m, we get:

2(x-1)=3

5. Apply Distributive property:

2x-2=3

6. Add 2 to both sides:

2x-2+2=3+2\\\\2x=5

7. Divide both sides of the equation by 2:

\frac{2x}{2}=\frac{5}{2}\\\\x=\frac{5}{2}

3 0
2 years ago
Read 2 more answers
Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36
Kamila [148]

A. 2x3=6 and 6x12=72 so 78 is greater than 36

6+72=79 which is less than 90

3 0
2 years ago
Read 2 more answers
What is the solution to the linear equation? 2.8y + 6 + 0.2y = 5y – 14 y = –10 y = –1 y = 1 y = 10
svp [43]

2.8y + 6 + 0.2y = 5y – 14

Simplify the left side:

3y +6 = 5y-14

Subtract 3y from both sides:

6 = 2y -14

Add 14 to each side:

2y =20

Divide both sides by 2:

y = 20 / 2

y = 10

5 0
2 years ago
Read 2 more answers
Which phrase describes only a square?
denis-greek [22]

Answer:

c is correct answer for you

5 0
2 years ago
Other questions:
  • Describe 58 as a sum of tens and ones.
    14·1 answer
  • Chuck chooses an investment plan that requires him to make a one-time investment of $10,000, and then equal monthly investments
    11·2 answers
  • Simplify x+2/x^2-6x-16 divided by 1/9x<br>a. 10x/x+4<br>b. x+4<br>c. 10x^2(x+2)/x+6<br>d. 9x/x-8
    15·1 answer
  • The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is .
    8·2 answers
  • The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2. Obi spent ?20 that day. Obi now had ?8 less than Rudy. How
    5·2 answers
  • Two different linear functions are shown below with two points given from each function. Use slope-intercept form or point-slope
    10·2 answers
  • The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a st
    13·1 answer
  • Which graph shows data whose r-value is most likely closest to 1?
    14·2 answers
  • On monday maggie ran n miles on tuesday she ran 90% of the number of miles she ran on monday and on tuesday she ran 50% of the n
    9·1 answer
  • A restaurant owner was experimenting with the taste of her homestyle lemon drink. She started with 60 litres of water. She remov
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!